The big Limerick man played all 80 minutes against France on Sunday but damaged the knee with the full extent of the injury confirmed after a scan in Dublin on Monday.
Murray, who was stretchered off in Paris, is out for up to four weeks after also damaging a knee in the French game.
Eoin Reddan and Declan Ryan will come into the team to play Scotland with Tomas O’Leary and Mike McCarthy added to the squad ahead of Wednesday’s team announcement.
Kidney, annoyed by the penalty count in Paris on Sunday, has paid tribute to his players for their efforts against the French.
He said, “We did not go to Paris to draw, we went there to win and to represent the people of Ireland in the best way possible.
“That is why I am immensely proud of the boys. I think that we went at it hard but we could not get that win we were looking for.”
THREE of the four Irish provinces won Celtic League games at the weekend. Munster beat the Dragons 24-14 in Wales, Leinster won 22-6 away to Aironi and Ulster were 38-16 winners at home to Edinburgh. Connacht went down 38-10 at the Scarlets.